Not an implementation claim. This is a classification framework — the one that determines what any return stream (a paper’s, a fund’s, your own) is worth, since the three categories command fee structures an order of magnitude apart.
Definitions. Beta: return from passive market exposure — buyable for basis points. Alternative risk premia (ARP): returns from systematic, documented style exposures — momentum, value, carry, low-vol — implementable by rules, priced between index funds and hedge funds, and arguably compensation for bearing identifiable risks (crash risk for momentum, drawdown regimes for carry). Alpha: return unexplained by market and documented styles — scarce, decaying, and the only thing meriting performance fees. The practical point: these are residual categories from a regression, not marketing labels, and the regression is runnable by anyone.
The sorting regression
r_strategy − r_f = α + β_mkt·MKT + Σ β_i·ARP_i + ε
Regress the stream on market plus a standard style set (the factor-hub canon: value, momentum, quality, carry, low-vol as relevant to asset class). Read it in order: R² and the betas tell you what the stream is — a “market-neutral” fund loading 0.6 on momentum is an ARP product; α’s magnitude and its standard error tell you whether anything merits the name (α with a t of 1.3 on four years is a shrug, not a discovery); and ε’s behavior in stress months tells you whether the “alpha” is actually an unlisted tail-risk premium — smooth ε that gaps down in crises is short-vol exposure the factor set didn’t span.
The unglamorous corollary: run this on your own strategies. Stat-arb books that never met a factor regression are usually momentum-and-short-vol in a trench coat.
The migration: alpha decays into beta
The boundary moves one direction. Yesterday’s alpha (size effects in the ’80s, momentum in the ’90s, imbalance signals in the 2000s) becomes today’s documented premium becomes tomorrow’s cheap product — the post-publication decay literature is this migration measured. Two consequences: any alpha claim carries an implicit expiry, and the diligence question is what protects the residual (capacity limits, infrastructure, data access, execution quality) rather than whether it exists today; and the factor set is era-relative — α against the 1995 factor set contains things that are ARP against 2026’s. Every alpha estimate is conditional on a benchmark vintage, which papers rarely state and readers should.
What each category should cost — the fee arbitrage lens
The taxonomy’s cash value is fee diligence: beta at active fees is the classic mis-sale; ARP at 2-and-20 is the hedge-fund industry’s documented embarrassment (large fractions of aggregate hedge-fund returns regress onto mechanical style portfolios); and true α commands whatever the market bears, after the regression proves it. The same lens prices research: a paper whose strategy returns regress heavily onto known premia has documented an implementation, not a discovery — worth reading, not worth its claimed novelty.
Common ways the taxonomy fails its users in production
- Benchmark gaming: α manufactured by regressing against an incomplete factor set; add the obvious missing premium and it vanishes. (Reader’s move: add it.)
- Nonlinear exposures slip the net: option-selling and liquidity provision show low linear betas and severe conditional exposure — the regression needs stress-month inspection, not just full-sample fits.
- ARP implementation slippage: the documented premium and your investable version differ by the tradability gates; budgeting the paper premium as “beta you can buy” double-counts what implementation eats.
- Alpha-at-scale delusion: α measured at paper size, charged at fund size — capacity converts α to β through impact.
Questions to ask of any return stream
- What’s left after the standard regression — and what’s the stress-conditional residual?
- Which factor-set vintage was the benchmark, and would today’s set absorb more?
- What structurally protects the residual from migration?
- Is the fee proportional to the α term, or to the whole stream?
What our scoring captures
Papers that run this decomposition on their own strategies — reporting factor-adjusted alphas with honest benchmarks — occupy the rigor axis’s upper reaches; “we beat the market” without a factor regression is the genre’s most reliable low-rigor tell. The taxonomy is also the quadrant system’s economic shadow: Street Traders papers mostly document ARP; genuine α claims concentrate — and deserve maximum scrutiny — among the Holy Grail’s top scorers.
The premia themselves: factor tradability → · momentum’s families → · The residual’s price: capacity →